The discoveries leading to our present understanding of the glutathione peroxidases (GPxs) are recalled. The cytosolic GPx, now GPx1, was first described by Mills in 1957 and claimed to depend on selenium by Rotruck et al., in 1972. With the determination of a stoichiometry of one selenium per subunit, GPx1 was established as the first selenoenzyme of vertebrates. In the meantime, the GPxs have grown up to a huge family of enzymes that prevent free radical formation from hydroperoxides and, thus, are antioxidant enzymes, but they are also involved in regulatory processes or synthetic functions. The kinetic mechanism of the selenium-containing GPxs is unusual in neither showing a defined K_M nor any substrate saturation. More recently, the reaction mechanism has been investigated by the density functional theory and nuclear magnetic resonance of model compounds mimicking the reaction cycle. The resulting concept sees a selenolate oxidized to a selenenic acid. This very fast reaction results from a concerted dual attack on the hydroperoxide bond, a nucleophilic one by the selenolate and an electrophilic one by a proton that is unstably bound in the reaction center. Postulated intermediates have been identified either in the native enzymes or in model compounds.